半无限区域上常系数对流扩散方程的解析解

An Analytical Solution to Constant Coefficients Advection-diffusion Equation in the Semi-infinite Domain

主要在半无限区域内研究均匀介质、稳定流条件下的二维对流扩散方程的解析解,针对常系数下两个问题:采用Laplace变换和Fourier变换相结合,求得连续一致输入浓度的下对流扩散方程的解析解;变坐标变换和Laplace变换,求输入连续增长性质下对流扩散方程的解析解.在得出相应的解析解后,与已有的解析解进行和数值解进行比较.

This paper discusses the two-dimension advection-diffusion equation in a homogeneous and steady flow in the semi-infinite domain,and discusses the following two problems under the conditions of constant coefficients and variable coefficients respectively：,solution to continuous input concentration of uniform nature with the Laplace transform and Fourier transform,solution to continuous input concentration of increasing nature with moving coordinate system and Laplace transform.After these,we compare the analytical solutions with the published result in analytical solutions and numerical solutions.